Related papers: Killing spinors and hypersurfaces
In this note we generalize the methods of [1][2][3] to 5-dimensional Riemannian manifolds M. We study the relations between the geometry of M and the number of solutions to a generalized Killing spinor equation obtained from a 5-dimensional…
In this paper, the Dirac, twistor and Killing equations on Weyl manifolds with CSpin structures are investigated. A conformal Schr"odinger-Lichnerowicz formula is presented and used to show integrability conditions for these equations. By…
We generalise the notion of a Killing superalgebra, which arises in the physics literature on supergravity, to general dimension, signature and choice of spinor module and Dirac current. We also allow for Lie algebras as well as…
On a Lorentzian manifold the existence of a parallel null vector field implies certain constraint conditions on the induced Riemannian geometry of a space-like hypersurface. We will derive these constraint conditions and, conversely, show…
Riemannian Einstein solvmanifolds can be described in terms of nilsolitons, namely nilpotent Lie groups endowed with a left-invariant Ricci soliton metric. This characterization does not extend to indefinite metrics; nonetheless,…
We compute explicitly the Killing spinors of some ten dimensional supergravity solutions. We begin with a 10d metric of the form $\RR^{1,3}\times{\cal Y}_6$, where ${\cal Y}_6$ is either the singular conifold or any of its resolutions.…
This is a doctoral thesis on the application of techniques originally developed in the programme of characterisation of supersymmetric solutions to Supergravity theories, to finding alternative backgrounds. We start by discussing the…
We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In…
We develop a new framework for the study of generalized Killing spinors, where generalized Killing spinor equations, possibly with constraints, can be formulated equivalently as systems of partial differential equations for a polyform…
We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to…
We study the intrinsic geometry of hypersurfaces in Calabi-Yau manifolds of real dimension 6 and, more generally, SU(2)-structures on 5-manifolds defined by a generalized Killing spinor. We prove that in the real analytic case, such a…
We construct a global geometric model for the bosonic sector and Killing spinor equations of four-dimensional $\mathcal{N}=1$ supergravity coupled to a chiral non-linear sigma model and a Spin$^{c}_0$ structure. The model involves a…
We provide some examples of Killing superalgebras on 2-dimensional pseudo-Riemannian manifolds within the theoretical framework established in [SIGMA 21 (2025), 081, 61 pages, arXiv:2409.11306]. We compute the Spencer cohomology group…
In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an $n$ -dimensional differentiable manifold $M$ endowed with an equiaffine $ SL(n, R) $ -structure and discuss possible applications of…
Simply connected 3-dimensional homogeneous manifolds $E(\kappa, \tau)$, with 4-dimensional isometry group, have a canonical Spin$^c$ structure carrying parallel or Killing spinors. The restriction to any hypersurface of these parallel or…
We study the geometric structure of Lorentzian spin manifolds, which admit imaginary Killing spinors. The discussion is based on the cone construction and a normal form classification of skew-adjoint operators in signature $(2,n-2)$.…
The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation…
We present a complete classification of invariant generalised Killing spinors on three-dimensional Lie groups. We show that, in this context, the existence of a non-trivial invariant generalised Killing spinor implies that all invariant…
We study metric solutions of Einstein-anti-Maxwell theory admitting Killing spinors. The analogue of the IWP metric which admits a space-like Killing vector is found and is expressed in terms of a complex function satisfying the wave…
On a pseudo-Riemannian manifold $\mathcal{M}$ we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of…